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@ARTICLE{Speck:849786,
      author       = {Speck, Robert},
      title        = {{P}arallelizing spectral deferred corrections across the
                      method},
      journal      = {Computing and visualization in science},
      volume       = {19},
      number       = {3-4},
      issn         = {1433-0369},
      address      = {Berlin},
      publisher    = {Springer},
      reportid     = {FZJ-2018-03898},
      pages        = {75-83},
      year         = {2018},
      note         = {Online first},
      abstract     = {In this paper we present two strategies to enable
                      “parallelization across the method” for spectral
                      deferred corrections (SDC). Using standard low-order
                      time-stepping methods in an iterative fashion, SDC can be
                      seen as preconditioned Picard iteration for the collocation
                      problem. Typically, a serial Gauß–Seidel-like
                      preconditioner is used, computing updates for each
                      collocation node one by one. The goal of this paper is to
                      show how this process can be parallelized, so that all
                      collocation nodes are updated simultaneously. The first
                      strategy aims at finding parallel preconditioners for the
                      Picard iteration and we test three choices using four
                      different test problems. For the second strategy we
                      diagonalize the quadrature matrix of the collocation problem
                      directly. In order to integrate non-linear problems we
                      employ simplified and inexact Newton methods. Here, we
                      estimate the speed of convergence depending on the time-step
                      size and verify our results using a non-linear diffusion
                      problem.},
      cin          = {JSC},
      ddc          = {570},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / DFG project 450829162 - Raum-Zeit-parallele
                      Simulation multimodale Energiesystemen (450829162)},
      pid          = {G:(DE-HGF)POF3-511 / G:(GEPRIS)450829162},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000439461000002},
      doi          = {10.1007/s00791-018-0298-x},
      url          = {https://juser.fz-juelich.de/record/849786},
}